The volume of the cone illustrated will be 117.2 unit³.
How to illustrate the information?From the information illustrated, the glass inform of a the frustrum of a cone has the dimensions: radius 4cm and a height of 7cm.
It should be noted that the volume of a cone is calculated as:
= 1/3 πr²h.
where,
π = 3.142
r = radius = 4cm
h = height = 7cm
In this case, since we know the values of the dimensions, then we can calculate the volume. This will be:
= 1/3πr²h
= 1/3 × 3.14 × 4² × 7
= 117.2 unit³
Therefore, the volume of the shape is 117.2 unit³.
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Complete question:
A glass inform of a the frustrum of a cone has the following dimensions: radius 4cm and a height of 7cm. Calculate the volume of the shape.
Steve took a 300 mile business trip and decided to travel by car. He drove the speed limit for half the trip until an accident occurred and he had to stop for a few hours in traffic. Steve then decided to drive slower than the speed limit the rest of the way to be safe. This situation models which type of function?
Based on the fact that Steve was originally driving the speed limit and then stopped a few hours and drove slower, the situation models a piecewise defined function.
What is a piecewise defined function?This is a type of function where there are two or more parts joined together. In other words, there are two equations to represent the different parts of the function.
In this case, Steve was driving at a certain speed. This is one function. Then he stopped for a couple of hours which is another function. Then the last function has him driving slower than the speed limit.
In conclusion, this is a defined piecewise function.
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the tens digit of a 2 digit number is 5 greater than the units digit if you subtract twice the reverse number the result is one fourth the original
Answer:
The original number is 72.
Step-by-step explanation:
Let the number by
[A][B]
The reverse number is
[B][A]
Original number:
A = B + 5
[A][B] - 2[B][A] = [A][B]/4
10A + B - 20B - 2A = (10A + B)/4
8A - 19B = (10A + B)/4
32A - 76B = 10A + B
22A - 77B = 0
22(B + 5) - 77B = 0
22B + 110 - 77B = 0
-55B = -110
B = 2
A = B + 5 = 2 + 5 = 7
The original number is 72.
The reverse is 27.
Let's check.
"the tens digit of a 2 digit number is 5 greater than the units digit"
7 is 5 greater than 2,so 72 looks good so far.
"if you subtract twice the reverse number the result is one fourth the original"
The reverse number is 27. Twice 27 is 2 × 27 = 54.
Subtract 54 from 72: 72 - 54 = 18
18 is 1/4 of 72. It works.
Answer: the original number is 72
Which rule describes the relationship between the x- and y- coordinates on the following graph? Choose 1 answer:
(Choice A)
A
y
=
2
x
y=2xy, equals, 2, x
(Choice B)
B
y
=
x
+
2
y=x+2
Answer:
A
Step-by-step explanation:
given the points
(0, 0 ) , (2, 4 ) , (4, 8 )
note that the y- coordinate is twice the value of the x- coordinate , so
y = 2x
domain of f(x)=(1/4)^x
What is the domain of f(x)
O A. x>0
OB. All real numbers
O C. y>0
O D. x<0
? Need help asap
Answer: B
Step-by-step explanation:
The domain of a function is the set of x-values.
B) Using the two point above find the slope using the formula m =
y/₁y₁
x₂-1
C) Plug in your slope and one of the two points above into point-slope formy - y₁ = m(x-x₁)
D) Change above equation into slope-intercept form y = mx + b. (See page 5 in lesson 5.06).
16+20
The linear equations are y - 25 = 0.89(x - 20) and y = 0.89x + 7.2
The slope of the lineThe complete question is added as an attachment
The two points from the graph are (20, 25) and (38, 41)
The slope of the line is calculated using
m = (y2 - y1)/(x2 - x1)
Substitute the known values in the above equation
m = (41 - 25)/(38 - 20)
Evaluate
m =0.89
The linear equation in point slope formThis is calculated as:
y - y1 = m(x - x1)
Substitute the known values in the above equation
y - 25 = 0.89 * (x - 20)
Evaluate
y - 25 = 0.89(x - 20)
The linear equation in slope-intercept formWe have:
y - 25 = 0.89(x - 20)
Expand
y - 25 = 0.89x - 17.8
Add 25 to both sides
y = 0.89x + 7.2
Hence, the linear equations are y - 25 = 0.89(x - 20) and y = 0.89x + 7.2
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Mike drove 40 miles from his home to his office, and he then drove back home using the same route. The average speed on his return trip was 10 miles/hour more than the average speed on his trip to the office. The total time for the trip is represented by this expression, where x is the average speed on the trip from his home to his office.
The average speed on Mike’s drive home is represented by
x + 10
.
When Mike drives at an average speed of 55 mile/hour on his way home, it takes him approximately
1.6 hours
to drive to work and back.
Mike's speed driving to his office is 45 miles/hour, which is 10 miles less than his average speed driving back.
How is speed calculated?Speed is an average value of a scalar measurement of the distance covered over the time taken.
Speed is the equation, r = d/Δt, where r = speed or rate, d = distance, and Δt is the change in time.
Thus, when the distance covered by a traveler is divided by the time consumed, one can determine the average speed for the travel.
Data and Calculations:Distance from Mike's home to his office = 40 miles
Distance to and from = 80 miles (40 miles x 2)
Hours covered from office = 1.6 hours
Average speed for the trip = 50 miles/hour (80/1.6)
Average speed to return home = 55 miles/hour
Average speed to office = 45 miles/hour (55 - 10)
Thus, Mike's speed of driving to his office is 45 miles/hour.
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Question Completion:What is Mike's speed driving to his office?
how do you compare and contrast the steps of two different constructions using a compass?
In order to compare and contrast the steps of two different constructions using a compass, we simply take a note of the different steps followed in both the constructions.
How to compare and contrast the steps?
For both the constructions, observe the corresponding steps steps that have been performed in order.
Then, note down what similarity you find while constructing the two different constructions in the first step.
Once you know the the similarities, you can further trace down the differences in the procedure of the two constructions by observing the first step. This is how you can compare and contrast the first step of two different constructions using a compass.
This process can be followed for all the steps for comparing and contrasting two different constructions.
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Proofs and congruent triangles ( serious full answers only or 1 star and report )
Answer:
There are 5 ways to find if two triangles are congruent.
SSS- {Side Side Side Congruence.}
This law of congruence states that if we have two triangles, each with the same measures on each 3 sides it deems the triangles congruent.
SAS- {Side Angle Side Congruence.}
This law of congruence states that if we have two triangles, with 2 equal sides and one angle which is common among them; the triangles are congruent.
ASA- {Angle Side Angle Congruence.}
This law of congruence states that if we have two triangles, with 2 congruent angle measures and 1 congruent side; the triangles are indeed congruent.
AAS- {Angle Angle Side Congruence.}
You may be wondering how this law of congruence differs from the previous one. ASA refers to any two angles and the included side, whereas AAS refers to the two corresponding angles and the non-included side.
HL- {Hypotenuse Leg Congruence.}
This law of congruence states that if we have two triangles, with a common (congruent) leg and hypotenuse; the triangles are congruent.
I really hoped this helped, if it didn't leave a comment I am always open to feedback. If it did let me know, brainiest is always appreciated!
Hope you have a great rest of your day.
Answer:
Step-by-step explanation:
for completeness, here is the answer again:
1 Given is correct
2 Definition of right angle is correct
3 should be sum of interior angles in a triangle
4 is substitution
5 subtracting 90degree from left and right hand side
6 is definition of complementary angles
Part of the arena is being turned into a public darkroom. The floor needs covering in rubber tiles before work can begin on the dark room. The tiles are 20 cm by 30 cm. The dark room floor is 6 metres by 3 metres. Are 280 tiles enough? How many more/less tiles are needed?
The number of tiles used is 300 tiles.
According to the statement
We have given that:
The tiles are 20 cm by 30 cm. And the dark room floor is 6 meters by 3 meters.
And we have to find that the number of tiles used to prepare the dark room.
So, For this purpose we have to find the area of the room floor.
The area of the floor is 6 *3.
The area of the floor is 18 meter per square.
The area of the tile is 0.2*0.3
The area of the tile is 0.06 meter per square.
Now,
The number of tiles used is 18/0.06
The number of tiles used is 300.
So, The number of tiles used is 300 tiles.
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find the critical value for the given confidence level c and sample size n c=.90 n=21
The critical value for the given confidence level, c = 0.90 and n = 21 is [tex]t_c=1.725[/tex].
How to calculate the critical value for t-distribution?The critical value is calculated as follows:
For the given sample size n, find the degree of freedom (d.f)Where d.f = n - 1Using the t-distribution table, the critical value is obtained for the obtained d.f and the confidence level.Calculation:It is given that,
confidence level c = 0.90
sample size n = 21
Then,
degree of freedom,
(d.f) = n - 1 = 21 - 1 = 20
So, from the t-distribution table,
at d.f = 20 and the confidence level 0.90, the critical value is 1.725.
I.e., [tex]t_c[/tex] = 1.725
For this, α = (1 - 0.90)/2 = 0.05
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Let Xi = (i =1,2,3) be independently and normally distributed random variable with mean of 4 as variance i. state the distribution of the following random variable
i) V = X1+X2+X3
The sum of normally distributed random variables is also a normally distributed random variable.
Given [tex]n[/tex] random variables with [tex]X_i\sim\mathrm{Normal}(\mu_i,\sigma_i^2)[/tex], their sum is
[tex]\displaystyle\sum_{i=1}^n X_i \sim \mathrm{Normal}\left(\sum_{i=1}^n \mu_i, \sum_{i=1}^n \sigma_i^2\right)[/tex]
i.e. normally distributed with mean and variance equal to the sums of the means and variances of the [tex]X_i[/tex].
In this case, each of [tex]X_1,X_2,X_3[/tex] are normally distributed with [tex]\mu=4[/tex] and [tex]\sigma^2[/tex] = ... I'm not sure what you meant for the variance, so I'll keep it symbolic. Then
[tex]V = X_1+X_2+X_3 \sim \mathrm{Normal}(12, 3\sigma^2)[/tex]
Difference of Squares gives which complex factors for the expression +3?
A. (x+3i)(x-3i)
B. (x-i-√3)(x-i√3)
C. (x+3i)^2(x-3i)²
D. (x+i√3)(x-i√3)
The difference of squares is:
(x+i√3)(x-i√3)
So the correct option is the last one, D.
Which expression gives x^2 + 3?For a complex number:
[tex]Z = a + b*i[/tex]
We define the complex conjugate of Z as:
[tex]Z' = a - b*i[/tex]
Such that the product between the complex number and its complex conjugate gives:
[tex]Z*Z' = a^2 + b^2[/tex]
Now, of you look at option D, you can see we have the product of a number and its conjugate, then we can write the product and use the above rule to get:
[tex](x + i\sqrt{3} )*(x - i\sqrt{3} ) = x^2 + (\sqrt{3} )^2 = x^2 + 3[/tex]
Which is what we wanted to get, so that is the correct option.
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TIME REMAINING
44:36
Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)?
(0,6)
(0,–6)
(6,0)
(–6,0)
Answer:
d. (-6, 0)
Step-by-step explanation:
no explanation bc u need this quick
A book sold 42,600 copies in its first month of release. Suppose this represents 9.2% of the number of copies sold to date. How many copies have been sold to date?
Answer:
We lend 100% - 9.2% and this will equal 90.8%, then we will make this percentage of 42,600 which will give us 38,680 and we will add the 42,600 and this will give us a total of 81,460 copies.
Evaluate each expression if A=2
B=-3. C=-1. D=4
2d-a/b
Answer:
2 × 4 - 2 / -3
8-2/-3
6/-3
-2
Is the following relation a function?
Nisha collects comic books, and she convinced her friend Hakim to start collecting as well. Every week, they go to the store together, and they each buy a new comic book. This table shows how many books they each have:
By using the given table, we will get the linear equation:
h = n - 9
How to find the equation for Hakim?
We know that they always get comic books together, so always that Nisha's collection increases by one, Hakim's collection will also increase by one, so we will have a linear equation.
Now, if you look at the given table, you can see that Hakim's collection is always 9 units less than Nisha's collection, then the linear equation that models the relation between the two collections, h and n, is really straightforward, it will be:
Hakim's collection = Nisha's collection - 9
Using the variables, we get:
h = n - 9
That is the linear equation Hakim wanted.
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Answer:
h=n-9
Step-by-step explanation:
1. A foot contains 12 inches. 5 inches is what fraction of a foot?
Answer:
5/12
Step-by-step explanation:
a foot =12 inches
fraction of 5 inches=5/12
What is the domain of f(x)=(1/3)^x
Answer:
All Real Numbers
Step-by-step explanation:
The domain is all the x values for a function. As this function is not restricted in any way, the domain is all real numbers. You can put any number in for x and plot it on the graph.
AN aquariums dimension are 3 1/4 x 2ft x 1 3/4. what is the volume of the aquarium
The volume of the rectangular prism aquarium = 17 1/16 ft.
What is the Volume of a Rectangular Prism?Volume of a rectangular prism = (l)(w)(h), where:
Length of the prism = lWidth of the prism = wHeight of the prism = hThe aquarium is a rectangular prism. Its dimensions are given as:
Length (l) = 3 1/4 ft
Width (w) = 3 ft
Height (h) = 1 3/4 ft
Substitute
Volume of the rectangular prism aquarium = (3 1/4)(3)(1 3/4)
Volume of the rectangular prism aquarium = (13/4)(3)(7/4)
Volume of the rectangular prism aquarium = (13 × 3 × 7)/(4 × 4)
Volume of the rectangular prism aquarium = (273)/(16)
Volume of the rectangular prism aquarium = 17 1/16 ft.
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x+2y=5 and 4x+12y=-20 elimination method
Answer:
x=25 and y=-10
Step-by-step explanation:
x+2y=5 ..........(1)
4x+12y=-20.........(2)
using elimination method.
multiply equ(1) by 4 and equ(2) by 1
so we have
x+2y=5..........*4
4x+12y=-20.........*1
4x+8y=20................(3)
4x+12y=-20.............(4)
subtract eq(4) from (3) we have
-4y=40
y=-10
substitute y=-10 in equation (1)
we have:
x+2(-10)=5
x-20=5
x=25
need heeeelp please
Answer:
1) log7 (5*8)= log7(40)
2) log2(11) -log2(9)=log2(11/9)
3)2log9 2=log9(2^2)
Any help with this greatly appreciated.
Put the equation in standard linear form.
[tex]x'(t) + \dfrac{x(t)}{t + 5} = 5e^{5t}[/tex]
Find the integrating factor.
[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{t+5}\right) = e^{\ln|t+5|} = t+5[/tex]
Multiply both sides by [tex]\mu[/tex].
[tex](t+5) x'(t) + x(t) = 5(t+5)e^{5t}[/tex]
Now the left side the derivative of a product,
[tex]\bigg((t+5) x(t)\bigg)' = 5(t+5)e^{5t}[/tex]
Integrate both sides.
[tex](t+5) x(t) = \displaystyle 5 \int (t+5) e^{5t} \, dt[/tex]
On the right side, integrate by parts.
[tex](t+5) x(t) = \dfrac15 (5t+24) e^{5t} + C[/tex]
Solve for [tex]x(t)[/tex].
[tex]\boxed{x(t) = \dfrac{5t+24}{5t+25} e^{5t} + \dfrac C{t+5}}[/tex]
pls help me!!! #18-19
Answer:
18. Sqrt40 goes between 6 and 7.
19. Sqrt83 ~= 9
Step-by-step explanation:
For both of these problems, it's really useful to be very familiar with the perfect squares on the times table. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225...
On #18, we're looking at the sqrt40. This will be between sqrt36 and sqrt49, because 40 is between 36 and 49. But sqrt36 is 6 and sqrt49 is 7. So sqrt40 is between 6 and 7.
For #19, the sqrt83 is far closer to sqrt81 than it is to sqrt100. Sqrt81 = 9. So sqrt83 is very close to 9, it would round to 9 and not 10.
Justin recently drove to visit his parents who live 270
miles away. On his way there his average speed was 11 miles per hour faster than on his way home (he ran into some bad weather). If Justin spent a total of 9 hours driving, find the two rates.
Answer:
66 mph to visit55 mph to homeStep-by-step explanation:
An equation can be set up and solved based on the relation between the two speeds and the relation between time, speed, and distance.
Setuptime = distance/speed
Let x represent the (slower) speed on the way home. Then the total time for the round trip was ...
time going + time coming home = total time
270/(x +11) +270/x = 9
Solution30x +30(x +11) = x(x +11) . . . . . . multiply by x(x+11)/9
x^2 -49x -330 = 0 . . . . . . . . rewrite in standard form
(x -55)(x +6) = 0 . . . . . . . . factor
x = 55 or x = -6 . . . . . . . solutions to this equation; x < 0 is extraneous
Justin's rate on the way there was 66 mph; on the way home, it was 55 mph.
SOMEONE PLEASE HELLPPPP
Answer:
93.39
Step-by-step explanation:
So the sum of exterior angles of the convex octagon is: 360 degrees
This means if we add all the equations that represent each angle, we can set it equal to 360 and solve for x
[tex](x+14) + (2x-3) + (3x+8) + (3x+16) + (2x-17) + (3x-4) + (3x-12) + (6x)[/tex]
Group like terms
[tex](x+2x+3x+3x+2x+3x+3x+6x) + (14-3+8+16-17-4-12)[/tex]
Add like terms
[tex]23x+2[/tex]
Now let's set the sum of exterior angles to 360
[tex]23x+2 = 360[/tex]
Subtract 2 from both sides
[tex]23x=358[/tex]
Divide both sides by 23
[tex]x\approx 15.565[/tex]
So by looking at all these, it appears that 6x is the highest value, given that x is positive. The way I estimated, is approximately 15.5, whenever I saw an equation like x+14, I estimated it's about 2x, since 14 is not exactly, but close to 15.5. I did this with each polynomial given. You could also manually check each one
Original equation
6x
Subsitute
6(15.565)
Simplify
[tex]93.39[/tex]
with the law of indices simplify 3a²b×2ab
Answer:
6a³b²
Step-by-step explanation:
3 × 2 = 6
a²× a¹ = a³
b × b = b²
Calculus HW , will someone please teach me how to do this problem. thanks! 10 Points
Your answers seem to be on the right track. These online homework apps can be picky about the answer they accept, though.
Given [tex]f(x) = x^4 - 2x^2 + 3[/tex], we have derivative
[tex]f'(x) = 4x^3 - 4x = 4x (x^2 - 1) = 4x (x - 1) (x + 1)[/tex]
with critical points when [tex]f'(x) = 0[/tex]; this happens when [tex]x=0[/tex] or [tex]x=\pm1[/tex].
We also have second derivative
[tex]f''(x) = 12x^2 - 4 = 12 \left(x^2-\dfrac13\right) = 12 \left(x - \dfrac1{\sqrt3}\right) \left(x + \dfrac1{\sqrt3}\right)[/tex]
with (possible) inflection points when [tex]x=\pm\frac1{\sqrt3}=\pm\frac{\sqrt3}3[/tex].
Intercept
If "intercept" specifically means [tex]y[/tex]-intercept, what you have is correct. Setting [tex]x=0[/tex] gives [tex]f(0) = 3[/tex], so the intercept is the point (0, 3).
They could also be expecting the [tex]x[/tex]-intercepts, in which case we set [tex]f(x)=0[/tex] and solve for [tex]x[/tex]. However, we have
[tex]x^4 - 2x^2 + 3 = \left(x^2 - 1\right)^2 + 2[/tex]
and
[tex]x^2-1\ge-1 \implies (x^2-1)^2 \ge (-1)^2 = 1 \implies x^4-2x^2+3 \ge 2[/tex]
so there are no [tex]x[/tex]-intercepts to worry about.
Relative minima/maxima
Check the sign of the second derivative at each critical point.
[tex]f''(-1) = 8 > 0 \implies \text{rel. min.}[/tex]
[tex]f''(0) = -4 < 0 \implies \text{rel. max.}[/tex]
[tex]f''(1) = 8 > 0 \implies \text{rel. min.}[/tex]
So we have two relative minima at the points (-1, 2) and (1, 2), and a relative maximum at (0, 3).
Inflection points
Simply evaluate [tex]f[/tex] at each of the candidate inflection points found earlier.
[tex]f\left(-\dfrac{\sqrt3}3\right) = \dfrac{22}9[/tex]
[tex]f\left(\dfrac{\sqrt3}3\right) = \dfrac{22}9[/tex]
Let f(x) = cxe−x2 if x ≥ 0 and f(x) = 0 if x < 0. For what value of c is f a probability density function? for that value of c find P(1
The value of c such that the function f is a probability density function is 2
How to determine the value of c?The density function is given as:
f(x) = cxe^(−x^2) if x ≥ 0
f(x) = 0 if x < 0.
We start by integrating the function f(x)
∫f(x) = 1
This gives
∫ cxe^(−x^2) = 1
Next, we integrate the function using a graphing calculator.
From the graphing calculator, we have:
c/2 * (0 + 1) = 1
Evaluate the sum
c/2 * 1 = 1
Evaluate the product
c/2 = 1
Multiply both sides of the equation by 2
c = 2
Hence, the value of c such that the function f is a probability density function is 2
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100 POINTS!!!!!!!!!!!!!!1 PLEASE SOLVE THESE PROBLEMS QUICKLY WITH AN EXPLANATION
In triangle ABC, if m∠B = 90°, BH = AH, and the ratio of m∠A to m∠C is 1:2, then m∠BHA = 120° (C).
In the next given equilateral triangle ABC, y = 70°.
Finding m∠BHA:
In triangle ABC, it is given that,
∠B = 90°
And m∠A : m∠C = 1:2
Let us assume m∠A is x. Then, m∠C = 2x
According to the angle sum property of a triangle,
∠A + ∠B + ∠C = 180°
90° + x + 2x = 180°
90° + 3x = 180°
3x = 90°
x = 30°
⇒ In triangle ABC, ∠A = 30° and ∠C = 60°
Now, in triangle AHB, it is also given that,
BH = AH
⇒ ∠ABH = ∠A = 30°
Thus, according to the angle sum property of a triangle,
∠ABH + ∠A + ∠BHA = 180°
30° + 30° + ∠BHA = 180°
∠BHA = 180° - 60°
∠BHA = 120°
Finding y in the Second Triangle:
Since triangle ABC is equilateral,
∠A = ∠B = ∠C = 60°
∴ x + 2x + 3x = 60°
6x = 60°
x = 10°
In triangle ABD, using angle sum property of triangle,
x + ∠B + ∠BDA = 180°
10° + 60° + ∠BDA = 180°
∠BDA = 180° - 70°
∠BDA = 110°
Now, since, ∠BDA and y are linearly adjacent angles,
∠BDA + y = 180°
110° + y = 180°
y = 180° - 110°
y = 70°
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